Method and apparatus for reducing the crest factor of a signal

ABSTRACT

A method and apparatus for reducing the crest factor of a signal uses a plurality of partial correction signals having respective predetermined frequencies. For each of the partial correction signals, the following steps are performed: (a) determining a time position of a maximum absolute amplitude of the signal; (b) calculating an amplitude and a phase depending on said maximum absolute amplitude and said time position for the respective partial correction signal; and (c) subtracting the respective partial correction signal from said signal to obtain a partially corrected signal which is used as the signal in step (a) for the next of the plurality of partial correction signals, and going to step (a) for calculating the next partial correction signal. The last-obtained partially corrected signal is output as the reduced-crest factor signal.

BACKGROUND

The present invention relates to a method and to an apparatus forreducing the crest factor (the ratio of peak to average value) of asignal, for example, a multi-carrier communication signal.

In recent years multi-carrier communication systems have been widelyused in particular for XDSL communication systems (Digital SubscriberLine) like ADSL (Asymmetric Digital Subscriber Line) or VDSL (Very HighSpeed Digital Subscriber Line). FIG. 1 illustrates a schematic blockdiagram of such a transmission system. A serial data signal a is fed toa serial/parallel converter 1 that converts the serial digital datasignal a into data packets with N/2 sub-packets, N being an even number.One data packet is transmitted in parallel to an encoder 2, whichassigns each sub packet to a separate carrier frequency and supplies afirst digital signal vector to an inverse Fourier transformer 3, whichperforms an inverse Fourier transformation on this vector and generatesa second digital signal vector comprising N samples of a signal to besent. This second digital signal vector is transmitted to aparallel/serial converter 23, which supplies the elements or samples ofthe second digital signal vector to a digital filter 24 followed by adigital-to-analog converter 25 and a line driver 26. The generatedanalog transmit signal is transmitted via a channel 27, whereby noise bis added, symbolized by an adder 28. On the receiver side, the signal isequalized by an equalizer/an analog-to-digital converter 29. Then thesignal is decoded by performing the reverse operations of the encodingelements 1 to 23, namely through a serial/parallel converter 30, aFourier transformer 31, a decoder 32, a slicer 33 and a parallel/serialconverter 34.

Such a communication system is for example disclosed in U.S. Pat. No.6,529,925 B1, the content of which is incorporated by reference herein.

Since the transmit signal is composed of a plurality of differentsignals having different carrier frequencies and amplitudes and phasesbeing determined by the data signal and thus having no predeterminedrelationships, the amplitude of the transmit signal has approximately aGaussian distribution. FIG. 2 illustrates the probability h of theamplitude A of the transmit signal as determined by a simulation for adiscrete multitone modulated transmit signal with a Fourier transformblock length of 256.

Because of this Gaussian distribution, the crest factor of the signal israther large, that is, the transmit signal has a rather high maximumamplitude value compared to the effective or average amplitude value.Since both the digital-to-analog and analog-to-digital converters, aswell as the line drivers, have to be adapted to handle the wholepossible amplitude range, these elements have to be defined accordinglycausing additional costs and chip space. It is therefore desirable toreduce the crest factor, that is to reduce the maximum amplitude.

In principle, two different approaches are known to reduce the crestfactor.

A first method for reducing the maximum amplitudes disturbs the transmitsignal. These methods comprise clipping methods as described for examplein U.S. Pat. No. 6,038,261.

A second method for reducing the maximum amplitude without disturbingthe signal.

In general, these methods use one or more of the carrier frequencies tomodify the transmit signal in order to reduce the maximum amplitude. Thecarrier frequencies used for this purpose may or may not only partiallybe used for the actual data transmission.

One of these methods is described in the already cited U.S. Pat. No.6,529,925 B1. There, the Nyquist frequency is used as a single carrierfrequency for correction purposes, that is, the last frequency in theinverse Fourier transform. In an ADSL signal, this frequency is not usedfor data transmission so that the correction does not influence thetransmission capacity. However, the performance of this method islimited since only a single carrier frequency is used for correction.Furthermore, this method is not applicable to VDSL signals since theNyquist frequency is outside the usable frequency range both fordownstream and for upstream transmission.

In U.S. Pat. No. 6,424,681 B1 a method for reducing the crest factorusing a plurality of carrier frequencies is disclosed. These carrierfrequencies are preferably evenly distributed over the whole usablefrequency range. From these carrier frequencies a normalized correctionsignal, a so-called kernel, is generated which has a “Dirac”-like shape,that is, a shape that comprises a single peak as far as possible. Tocorrect a transmit signal, this correction signal is phase shifted tothe position of the maximum of the transmit signal and then scaled witha suitable scaling factor depending on the maximum amplitude of thetransmit signal. Then, this correction signal is subtracted from thetransmit signal. This can be repeated several times to iterativelycorrect several maximum or peak values. For transmission systems with agreat number of carrier frequencies and consequently a great number ofsignal values in each frame, like a VDSL transmission system, thismethod is difficult to realize since it needs a relatively longcomputation time. Furthermore, through the use of a kernel, the carrierfrequencies used for the correction have to comprise both low and highfrequencies which, consequently, are not usable for data transmission.The use of low carrier frequencies, on the other hand, leads to agreater loss of transmission capacity since lower carrier frequenciescan be modulated with more bits than high carrier frequencies due to thelower damping.

SUMMARY

One embodiment of the present invention provides a method and anapparatus that effectively reduce the crest factor using a limitednumber of carrier frequencies. Furthermore, one embodiment provides sucha method and such an apparatus that are usable for VDSL transmission.

According to one embodiment of the invention, for reducing the crestfactor of a signal using a plurality of partial correction signalshaving predetermined frequencies, the following steps are carried out:

(a) determining a time position of a maximum absolute amplitude of thesignal,

(b) calculating an amplitude and a phase for the respective partialcorrection signal depending on said maximum absolute amplitude and saidtime position determined in step (a),

(c) subtracting the respective partial correction signal from saidsignal to obtain a partially corrected signal which is used as thesignal in step (a) for the next one of the plurality of partialcorrection signals, and returning to step (a) for calculating anamplitude and a phase for the next partial correction signal,

said method further comprising the step of

(d) outputting the last obtained partially corrected signal as thecorrected signal having the reduced crest factor.

As for each of the predetermined frequencies, i.e. carrier frequencies,an amplitude and a phase is calculated, and it is possible to use thepredetermined frequencies available in an optimum manner to correct thesignal.

Steps (a) to (c) may be repeated a given number of iterations to obtaineven better results.

In step (b), the amplitude may be calculated according toA=g·(max {X(t)·cos(2πf(t−t max))}+min {X(t)·cos(2πf(t−t max))})A being the amplitude, g being a predetermined factor, f being therespective predetermined frequency, t being the time, t max being saidtime position, X(t) being said signal and max and min designate themaximum and minimum operator, respectively. The phase accordinglyamounts to 2πf·t max.

For discrete multitone modulation signals as mentioned in theintroductory portion, the signal may be represented as a signal vectorof signal values at N sampling times. Accordingly, the above formula maybe reformulated basically by replacing the time by the number of thesample and replacing the frequency by a number of the frequency dividedby N.

The method as described so far is suitable for signals where the signalvector does not comprise too many samples. For transmission systems likeVDSL systems carrying out the described method in full would costconsiderable calculation time.

Therefore, instead of performing the above method on the signal or on avector representing the signal, one embodiment performs the method on avector containing only a predetermined number of maximum amplitudevalues of the signal. This predetermined number may be significantlylower than the number of samples in the actual signal vector, thereforesaving considerable calculation time while only marginally lowering theperformance. To do this, the positions of the elements of the vectorwith the maximum amplitude values in the original signal vector have tobe stored since the final correction has to be performed on the signalitself.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are included to provide a furtherunderstanding of the present invention and are incorporated in andconstitute a part of this specification. The drawings illustrate theembodiments of the present invention and together with the descriptionserve to explain the principles of the invention. Other embodiments ofthe present invention and many of the intended advantages of the presentinvention will be readily appreciated as they become better understoodby reference to the following detailed description. The elements of thedrawings are not necessarily to scale relative to each other. Likereference numerals designate corresponding similar parts.

FIG. 3 illustrates an embodiment of an apparatus for reducing a crestfactor of a signal according to the present invention.

FIGS. 4A and 4B illustrates simulations of the performance of the methodof the present invention for ADSL signals.

FIGS. 5A and 5B illustrate further simulations of the performance of themethod of the present invention for ADSL signals.

FIGS. 6A and 6B illustrate usable frequency ranges for VDSL in adownstream and in an upstream direction, respectively.

FIGS. 7A and 7B illustrate simulation results for VDSL upstream.

FIGS. 8A and 8B show simulation results for VDSL downstream.

FIG. 1 illustrates a standard multi-carrier transmission system.

FIG. 2 illustrates an amplitude probability distribution for a standardmulti-carrier transmission system.

DETAILED DESCRIPTION

As already described in the introductory portion with reference to FIG.1, a transmit signal in a multitone transmission like discrete multitonetransmission comprises a number of samples derived from parallelprocessing of a number of bits of serial data, a data block. Thistransmit signal may be described as a vectorX ^(T) =[x(1),x(2), . . . ,x(N)],  (1)N being the number of samples and x(n) being the respective samples, nranging from 1 to N. The index n thus denotes the time position of therespective sample. “T” indicates that the vector in equation (1) iswritten in a line instead of in a column.

One embodiment of the present invention is to determine a correctionvector Xk so that the maximum absolute value or amplitude of theelements of the vector Xs withXs=X−Xk  (2)

assumes a minimum value. The correction vector Xk is a superposition ofseveral partial correction vectors corresponding to a number of carrierfrequencies or carrier tones reserved for forming the correction vectorXs, i.e.

$\begin{matrix}{{{Xk} = {\sum\limits_{i = 1}^{Nt}{Xk}_{i}}},} & (3)\end{matrix}$Nt being the number of carrier frequencies reserved for correction.Xk_(i) denotes the i-th correction vector contribution of carrierfrequency number i.

In general, the components of Xk_(i) may be written as

$\begin{matrix}{{{{xk}_{i}(k)} = {{{a_{i}(\mu)}{\cos\left( {2{{\pi\mu} \cdot \frac{k - 1}{N}}} \right)}} + {{b_{i}(\mu)}{\sin\left( {2{\pi\mu}\frac{k - 1}{N}} \right)}}}},} & (4)\end{matrix}$wherein k is the component or sample index of the vector, ranging from 1to N, and μ is the number of the respective carrier frequency used toform the correction vector xk_(i) assuming that all the carrierfrequencies used including those used for transmitting the actualinformation are numbered consecutively and are spaced evenly apart fromeach other, starting with 0. Such a numbering of carrier frequencies isusually used for example for the carrier frequencies of ADSL or VDSLtransmission. Generally, equation (4) is an oscillation with thefrequency determined by μ and an amplitude and phase determined by a_(i)and b_(i).

In the following, an iterative procedure for correcting the vector X andfor determining the correction vector Xk is given, comprising thefollowing steps:

1. determining the element of the vector X having the maximum absoluteamplitude |X(k max)| and its position within the vector X k max, and

2. forming an auxiliary vector Xh according to

$\begin{matrix}{{{{{xh}(k)} = {{x(k)}{\cos\left( {2{\pi\mu}\frac{k - {k\mspace{14mu}\max}}{N}} \right)}}};{k = 1}},2,{\ldots\mspace{11mu} N},} & (5)\end{matrix}$xh being the components of Xh. Since the cosine term for k=k max isequal to 1, the auxiliary vector has the element with the same maximumabsolute amplitude at the same position k max as the vector X.

3. For the carrier frequency μ, a partial correction is carried outaccording to:

$\begin{matrix}\begin{matrix}{{x(k)}_{new} = {{x(k)}_{old} - {{g\left( {{\max\left\{ {{xh}(k)} \right\}} + {\min\left\{ {{xh}(k)} \right\}}} \right)} \cdot}}} \\{{0.5 \cdot \cos}\left( {2{\pi\mu}\frac{k - {k\mspace{14mu}\max}}{N}} \right)} \\{{k = 1},2,\ldots\mspace{11mu},N,}\end{matrix} & (6)\end{matrix}$wherein the indices “new” and “old” indicate that the elements of thevector X are replaced by the new elements. In equation (6), max is themaximum operator yielding the maximum value of all the xh(k) and mm isthe corresponding minimum operator. In general, the minimum will be anegative value. It should be noted in this respect that the maximumabsolute amplitude determined in step 1 may be either the maximum or theminimum value. The factor g is an appropriate converging factor whichmay be chosen to be 1 or may vary from iteration to iteration asexplained below. The factors 0.5 and g may be drawn into a singlefactor.

4. also given is repeating steps 1 to 3 for all carrier frequencies μused for correcting the signal, whereby the “new” vector X is used forthe respective next carrier frequency.

5. also given is repeating steps 1 to 4 L times. The converging factor gcan be chosen to decrease from iteration to iteration ensuring a betterconvergence.

The total correction vector Xk would then be a sum of all thecorrections carried out in step 3.

The vector X^(T)=[x(1),x(2), . . . ,x(N)] resulting from this method hasthe smallest maximum absolute amplitude possible with a correctionsignal consisting of the given correction carrier frequencies.

On the other hand, for vectors X having a large number of elements thisalgorithm needs a large realization effort since for each iteration foreach carrier frequency used for correction a correction term has to besubtracted componentwise from the original vector X. For example, for aVDSL transmission vector the vector X has 8192 elements.

Therefore, a simplification of the above algorithm is needed for vectorsX having a large number of elements. The general idea for simplifyingthe above algorithm is not to perform the algorithm on the completevector X, but on an auxiliary vector Xm^(T)=[xm(1),xm(2), . . . ,xm(M)]comprising the M elements having the largest absolute amplitudes of thevector X, M being much smaller than N. For example, for VDSL systems Mmay be chosen to be 32 which is considerably smaller than 8192, thussaving considerably computation time. Since the correction itself has tobe performed on the whole signal, that is on the vector X, a furtherauxiliary vector Pm^(T)=[pm(1), pm(2), . . . , pm(M)] is needed forstoring the positions of the elements of the vector Xm within the vectorX, i.e. xm(k)=x(pm(k)).

An algorithm for determining the vectors Xm and Pm will be given later.

In the following, it will be shown how the algorithm described above hasto be performed using the vector Xm. The following steps have to becarried out corresponding to the respective steps of the algorithmalready explained:

1. the position k max of the element of the vector Xm having the largestabsolute amplitude or value |xm(k max)| is determined and

2. an auxiliary vector Xmh according to

$\begin{matrix}\begin{matrix}{{{{xmh}(k)} = {{xm}{(k) \cdot {\cos\left( {2{\pi\mu}\frac{{{pm}(k)} - {{pm}\left( {k\mspace{14mu}\max} \right)}}{N}} \right)}}}};} \\{{k = 1},2,\ldots\mspace{11mu},M}\end{matrix} & (7)\end{matrix}$is calculated, wherein the xmh are the components of the vector Xmh.Thus, through the use of the vector Pm within the cosine term, thecosine term assumes the “correct” values for the elements of the vectorXm that correspond to the values of the correction finally performed onthe whole signal X.

3. A partial correction corresponding to the one for the full vector Xis carried out:

$\begin{matrix}\begin{matrix}{{{xm}(k)}_{new} = {{{xm}(k)}_{old} - {g \cdot \left( {{\max\left\{ {{xmh}(k)} \right\}} + {\min\left\{ {{xmh}(k)} \right\}}} \right) \cdot}}} \\{{{0.5 \cdot \cos}\left( {2{\pi\mu}\frac{{{pm}(k)} - {{pm}\left( {k\mspace{14mu}\max} \right)}}{N}} \right)};} \\{{k = 1},2,\ldots\mspace{11mu},{M.}}\end{matrix} & (8)\end{matrix}$

After performing the algorithm the correction vector Xk for the signalvector, X has to be calculated. To this end, it is helpful to store foreach partial correction and for each frequency μ the correctionamplitudeΔu(i,j)=g·(max {xmh(k)}+min {xmh(k)})·0.5,  (9)and the corresponding phaseΔp(i,j)=pm(k _(max)),  (10)wherein i is again the number of the carrier frequency as in equation(4) and j is the number of the iteration.

4. steps 1 to 3 for all carrier frequencies μ used for the correctionsignal or vector, and

5. steps 1 to 4 L times, possibly with decreasing converging parameterg.

At the end of this procedure, an auxiliary vector Xm having a minimalmaximum absolute amplitude is obtained. From the stored amplitude andphase values Δu(i,j) and Δp(i,j), the amplitudes and phases for thefinal correction vector Xk with N components can be calculated. Eachpartial correction vector for a single correction carrier frequency μcan be calculated according to equation (4). The respective correctionamplitudes a_(i)(μ) and b_(i)(μ) can be calculated as follows:

$\begin{matrix}{{{a_{i\;}(\mu)} = {\sum\limits_{j}{\Delta\;{u\left( {i,j} \right)}{\cos\left( {2{\pi\Delta}\;{{p\left( {i,j} \right)} \cdot \frac{\mu}{N}}} \right)}}}}{b_{i\;}(\mu)} = {\sum\limits_{j}{\Delta\;{u\left( {i,j} \right)}{{\sin\left( {2{\pi\Delta}\;{p\left( {i,j} \right)}\frac{\mu}{N}} \right)}.}}}} & (11)\end{matrix}$

Alternatively, the amplitudes a_(i)(μ) and b_(i)(μ) may be computediteratively in step 3 of the algorithm given above, so that the Δu andΔp do not have to be stored. In this case, in step 3, the followingcalculations have to be performed:

$\begin{matrix}{{{a_{i\;}(\mu)}_{new} = {{a_{i}(\mu)}_{old}\; + {\Delta\;{{u\left( {i,j} \right)} \cdot {\cos\left( {2{\pi\mu}\frac{\Delta\; p\left( {i,j} \right)}{N}} \right)}}}}}{b_{i\;}(\mu)}_{new} = {{b_{i}(\mu)}_{old} + {\Delta\;{{u\left( {i,j} \right)} \cdot {{\sin\left( {2{\pi\mu}\frac{\Delta\; p\left( {i,j} \right)}{N}} \right)}.}}}}} & (12)\end{matrix}$

The correction vector is composed of cosine and sine values weighed withrespective amplitude values. The cosine and sine values can be read froma sine table or a cosine table. One table is sufficient for the cosineand the sine values since its two functions only differ in the phase,that is the respective address of the table read out has to be adapted.The use of such a sine table makes the algorithm faster compared toexplicitly calculating the sine or cosine values each time.

A reduction of the values to be stored in such a table can be obtainedif the sine or cosine value is calculated as an interpolation, forexample a linear interpolation, between stored sine values. It hasturned out that the storage of 32 sine values of a quarter period issufficient. The remaining three quarters of the period of the sine andcosine functions can be calculated using the symmetry of thesefunctions.

It is possible to write the partial correction vector Xk_(i) also as

$\begin{matrix}{{{xk}_{i}(k)} = {{c_{i}(\mu)}{\cos\left( {{2{\pi\mu}\frac{k - 1}{N}} + {\varphi_{i}(\mu)}} \right)}\mspace{14mu}{with}}} & (13) \\{{{c_{i}(\mu)} = \sqrt{{a_{i}^{2}(\mu)} + {b_{i}^{2}(\mu)}}};\mspace{14mu}{{\varphi_{i}(\mu)} = {{\arctan\left( \frac{b_{i}(\mu)}{a_{i}(\mu)} \right)}.}}} & (14)\end{matrix}$

arctan being the arcus tangens operator.

In this case, only a single sine value has to be calculated or read outfrom the sine table for each partial correction vector with the carrierfrequency μ. The values for c_(i)(μ) and φ_(i)(μ) from equation (14) mayalso be calculated using the known Cordic algorithm. This algorithm isused for calculating amplitude of a phase of a complex number when itsreal end imaginary part is given. As a real part a_(i) and as imaginarypart b_(i) can be taken. The Cordic algorithm is an iterative algorithmthat uses only additions and subtractions as well as the sign functionfor determining the sine of a number. For performing the algorithm, Larcus tangens values have to be stored, L being the number of iterationsof the Cordic algorithm. After carrying out the Cordic algorithm theamplitude of the respective complex number which results from thealgorithm is enlarged by a fixed factor dependent on L. Therefore, it isnecessary to divide this value by this factor. To be able to omit thesedivisions, the values of the sine table may be divided by the factor inadvance.

A further reduction of computing effort can be obtained if the storedvalues of the sine table, for example 32 values, are multiplied with therespective amplitude of the correction carrier frequency in advance andstored in an intermediate storage. For computing the partial correctionvector this intermediate storage would simply have to be addressed. Nofurther multiplication would be necessary.

The realization effort can be further reduced significantly by choosingthe carrier frequencies used for correction in an appropriate manner.If, for the representation of equation (13), the carrier frequency ischosen asμ=2^(l) ·v  (15)and the number of elements in the vector X isN=2^(n)  (16)which is generally the case for system using inverse fast Fouriertransform like the system described in the introductory portion,equation (14) transforms to

$\begin{matrix}{{{xk}_{i}(k)} = {{c_{i}(\mu)}{\cos\left( {{2{{\pi 2}^{\ell} \cdot v \cdot \frac{k - 1}{2^{''}}}} + {\varphi_{i}(\mu)}} \right)}\mspace{14mu}{or}}} & (17) \\{{{{xk}_{i}(k)} = {{c_{i}(\mu)}{{\cos\left( {{2{\pi \cdot v \cdot \frac{k - 1}{2^{n - \ell}}}} + \varphi_{\mu}} \right)}.}}}\mspace{14mu}} & (18)\end{matrix}$

As can be easily seen, the partial correction vector Xk_(i) is periodicwith a period of 2^(n−l). If the different carrier frequencies used forcorrection differ only in the value v, the resulting correction vectorXk only has to be calculated for the first 2^(n−l) values. The wholecorrection vector is then obtained through periodic continuation.

For the simplified algorithm, as stated above, the auxiliary vector Xmis needed containing the M values of the vector X having the largestabsolute amplitude values. A possible algorithm for obtaining the vectorXm and the vector Pm comprises the following steps:

1. The vector Xm is initialized to contain the M last elements of thevector X, that is,xm(k)=x(N−M+k); k=1,2, . . . , M.  (19)

2. The vector Pm is initialized accordingly, that is,pm(k)=N−M+k; k=1,2, . . . , M.  (20)

3. A counter λ is set to 0: λ=0.

4. The element of the vector Xm having the smallest absolute value isdetermined:x min=min {|xm(k)|}  (21)

x min being that minimum value.

5. The corresponding position k min is determined:k min=Position of min {|^(xm)(k)|}; that is,|xm(k min)|=min {|xm(k)|}.  (22)

6. The counter λ is incremented: λ=λ+1.

7. The element of the vector X designated by the counter λ is comparedwith x min; steps 6 and 7 are repeated until|x(λ)|>x min.

8. When |x(λ)|>x min is fulfilled, the minimal element of the vector Xmis replaced by the element of the vector X designated by the counter λ,and the corresponding element of the vector Pm is replaced by λ, thatis,xm(k min)=x(λ)pm(k min)=λ.

9. The procedure is continued at step 6 until λ has reached the valueN−M

When this procedure is completed, the vector Xm contains the M valueshaving the largest absolute amplitudes of the vector X, and the vectorPm contains the corresponding positions.

The time needed for performing this algorithm depends on the arbitraryvalues of the starting vector for Xm. The more large values this vectorcontains when starting the procedure, the less often the contents of thevector Xm has to be overwritten and the minimum element of the vector Xmbe determined. Consequently, through a pre-sorting of the vector X it ispossible to optimize this algorithm.

FIG. 3 illustrates an apparatus suitable for carrying out the method ofthe present invention corresponding to the algorithms described above. Adata signal a is supplied to a serial-to-parallel converter 1 andmodulated onto a number of carrier frequencies wherein a predeterminednumber of carrier frequencies are not used for transmitting the data,but for building the correction signal as described above. On the thusgenerated signal, an inverse Fourier transform is performed in element3, and the data is supplied to a parallel-to-serial converter 23, whichis generally used for serially outputting the corresponding signalvector. Up to this point, the apparatus corresponds to the one alreadydescribed with reference to FIG. 1 above, that is, in converter 23 thevector X is stored. The vector X is transmitted to means 4 fordetermining the maximum amplitude x max of the elements of the vector X. Comparing means 5 compare this maximum value x max with a givenreference value x ref . If x max is below x ref, switches 6 and 7 areopened, meaning that no correction algorithm is performed as the maximumvalue x max is below x ref which represents a maximum tolerable valuefor the amplitudes or values of the vector X. In this case, the vector Xis output via a subtractor 35 unchanged, since switch 7 supplying thenegative input of subtractor 35 is opened.

If however, x max exceeds xref, the switches 6 and 7 are closed. Viaswitch 6, the vector X is supplied to sorter 8 which, with the help ofthe parameter M already described above, determines the auxiliaryvectors Xm and Pm which are supplied to calculator 9. Calculator 9performs the above-described iterative algorithm on the vector Xm andthen computes the amplitude and phase values c_(i) and φ_(i) using thefrequencies μ allocated for correction. At most L iterations areperformed. If, however, x max falls below xref cefore the L interationsare performed, the algorithm is terminated and the values for c_(i) andφ_(i) are output. In vector builder 10, the total correction vector Xkis built as described above and supplied via switch 7 to the subtractor35 where it is subtracted from the vector X.

It should be noted in this respect that the vector representation servesas a means for easily representing the signals. However, the wholeprocedure may as well be viewed as carried out using the signalsthemselves, that is, emitting corresponding correction signals havingthe respective frequencies μ.

It is possible to use less frequencies μ for correcting the signals thanactually allocated. For example, twelve frequencies may be allocated forcorrection, two of three of them may be used. These two or threefrequencies should be changed from vector X to vector X, i.e. from frameto frame, to distribute the power of the correction signal over allcorrection frequencies.

Therefore, it is necessary to modify the algorithm slightly. If afterthe L-th iteration x max is still greater than xref, the procedure isrepeated with a different choice of correction frequencies. If this isnot the case after a certain number of tries, the frequencies whichyielded the smallest value x max are used.

In the following, the performance of the method according to theinvention will be demonstrated using simulation results.

EXAMPLE 1 Downstream Transmission in an ADSL System

For the inverse fast Fourier transform in ADSL systems generally 265frequency values which are equally spaced from 0 to half the samplingfrequency are defined. Therefore, a frame or vector X comprises 512signal values, that is, N=512. The distance between carrier frequenciesis 4.3125 KHz, resulting in a sampling frequency of 2.208 MHz. For datatransmission the frequencies numbers 33 to 255 are used (142.3 to 1100KHz). Two different sets of parameters were simulated. The firstsimulation was performed using frequency numbers 254, 217, 247, 225,239, 231, 210 and 243 for correction purposes. M was set to 8, L, themaximum number of iterations, also to 8. xref was set to 4.1. The powerof the signal was normalized to 1, so that the peak value corresponds tothe crest factor.

FIGS. 4A and 4B illustrates the results for these values. FIG. 4Aillustrates the probability p for the occurrence of various crestfactors C given as a ratio, FIG. 4B illustrates the same graph with thecrest factor c given in decibel. Curve 11 shows the theoretical Gaussiandistribution. Curve 12 shows the result without correction. The reasonwhy curve 12 deviates from curve 11 is the limited simulation time, fora longer simulation time also the even higher crest factors wouldeventually occur. It can be seen that crest factors above 5.5 occur witha probability greater than 10⁻⁸.

Curve 13 shows the results using the method according to the presentinvention. It can be seen that the probability for a crest factor of 4.1or 12.25 dB is 10⁻⁸ corresponding to a reduction of 2.9 dB compared tothe non-corrected case of curve 12.

For a second simulation, only five carrier frequencies were used forcorrection, namely numbers 240, 224, 208, 192 and 176. These fivecarrier frequencies are evenly spaced apart resulting in a periodiccorrection signal or correction vector Xk with a period of 32. M and Lwere both set to 8 as in the first simulation, and xref was set to 4.3.The result as illustrated in FIGS. 5A and 5B corresponding to FIGS. 4Aand 4B of the first simulation. Curve 11 again is the theoreticalGaussian distribution, curve 14 is the uncorrected curve correspondingto curve 12 of FIGS. 4A and 4B, and curve 15 is the corrected curveusing the method of the present invention. The deviations between curves12 in FIGS. 4A and 4B and curves 14 in FIGS. 5A and 5B again stem fromthe statistical nature of the amplitude distribution and the limitedsimulation time. In this case, a crest factor of 4.4 corresponding to12.85 dB occurs with a probability of 10⁻⁸. Here, still a reduction of2.3 dB compared to the uncorrected curve is obtained.

Consequentialy, it can be seen that the method of the present inventionleads to a considerable reduction of the crest factor for ADSLtransmissions.

EXAMPLE 2 VDSL Transmission

In VDSL systems 4096 frequency values are equally spaced apart from 0 tohalf the sampling frequency, resulting in a frame or vector X having8192 values or elements. The distance between carrier frequencies is4.3125 KHz corresponding to the ADSL value, resulting in a samplingfrequency of 35.328 MHz.

For downstream and upstream transmission different frequency ranges aredefined, which are illustrated in FIGS. 6A and 6B. FIG. 6A illustratesthe frequencies reserved for downstream transmission corresponding tofrequencies number 257 to 695 and 1182 to 1634. FIG. 6B illustrates thefrequencies reserved for upstream transmission, that is, is frequencynumbers 696 to 1181 and 1635 to 2782.

First, a simulation for upstream transmission was performed.

Twelve possible carrier frequencies were allocated for correctionpurposes, frequencies number 2688, 2624, 2560, 2496, 2432, 2368, 2304,2240, 2176, 2112, 2048, 1984. Three of these frequencies were used foractual correction. The allocated carrier frequencies are equally spacedapart and have a distance of 64 (i.e. 64×4.3125 KHz), resulting in acorrection signal having a period of 128 independent of the actualchoice of the three carrier frequencies used for correction. Asparameters for the method of the present invention M=32 , xref=4.3 andL=8 were used. A maximum number of twelve choices of the three carrierfrequencies were tried for each correction.

FIGS. 7A and 7B illustrates the simulation results, the representationof the results again being similar to those of FIGS. 4 and 5. Curve 11again represents the theoretical Gaussian distribution, curve 16 thesignal without correction and curve 17 the signal with correctionaccording to the method of the present invention. A probability of 10⁻⁸corresponds to a crest factor of 4.5 or 13 dB according to curve 17,which again is a considerable reduction compared to the 5.6 or 15 dB ofthe uncorrected curve 16.

For a downstream simulation, six carrier frequencies were used, namelyfrequencies number 1600, 1536, 1472, 1408, 1344 and 1280. The distancebetween the carrier frequencies again is 64, which again results in aperiodic correction signal having a period of 128. For the simulation,the parameters M=32, xref=4.3 and L=8 were used. FIGS. 8A and 8Billustrate the results of this simulation. Curve 18 is the resultwithout correction, curve 19 is the result with the correction accordingto the present invention. A probability of 10⁻⁸ corresponds to a crestfactor of 4.65 or 13.4 dB, again yielding a significant improvementcompared to the uncorrected signal.

It should be noted that the simulation examples given above are onlygiven as an illustration, and other parameters may be used depending onthe amount of crest factor reduction needed and the amount ofcomputation time possible. For example, a larger value of M generallyleads to a better reduction of the crest factor, but needs morecalculation time. Other carrier frequencies than the one used in thesimulations may be allocated for correction purposes.

Although exemplary embodiments of the invention are described above indetail, this does not limit the scope of the invention, which can bepracticed in a variety of embodiments.

1. A method for reducing the crest factor of a signal, said method usinga plurality of partial correction signals having respectivepredetermined frequencies, said method comprising: (a) determining atime position of a maximum absolute amplitude of the signal, (b)calculating an amplitude and a phase for the respective partialcorrection signal depending on said maximum absolute amplitude and saidtime position determined in step (a), (c) subtracting the respectivepartial correction signal from said signal to obtain a partiallycorrected signal which is used as the signal in step (a) for the nextone of the plurality of partial correction signals, and returning tostep (a) for calculating an amplitude and a phase for the next partialcorrection signal, and (d) outputting the last obtained partiallycorrected signal as the corrected signal having the reduced crestfactor.
 2. The method according to claim 1, wherein steps (a) to (c) arerepeated for at least two iterations for each one of the plurality ofpartial correction signals.
 3. The method according to claim 2, where amaximum number of iterations is predetermined.
 4. The method accordingto claim 2, wherein steps (a) to (c) are repeated for each one of theplurality of partial correction signals until a maximum absoluteamplitude of the partially corrected signal is below a predeterminedvalue.
 5. The method according to claim 1, wherein step (b) comprisesthe steps of (b1) calculating said amplitude according to A=g·(max{x(t)·cos(2πf(t−t max))}+min {x(t)·cos(2πf(t−t max))}), A being theamplitude, g being a predetermined factor, f being the respectivepredetermined frequency, t being the time, t max being said timeposition and x(t) being said signal, and (b2) calculating said phase paccording to p=2πf·t max.
 6. The method according to claim 1, whereinthe signal is a sampled signal represented as a signal vector of Nsignal values at N sampling times.
 7. The method according to claim 6,wherein step (b) comprises the steps of (b1) calculating said amplitudeaccording to the formulaA=g·(max {x(k)·cos(2πμ(k−k max)/N)}+min(x(k)·cos(2πμ(k−k max)/N)}), Abeing the amplitude, g being a predetermined factor, μ being a number ofthe respective predetermined frequency, k being a number of the sample,k max being this number of the sample at said time position, and x(k)being a k-th component of said signal vector, and (b2) calculating saidphase p according to p=2πμ·k max/N.
 8. The method according to claim 7,wherein values for μ have the form 2^(l)·v, l and v being integernumbers.
 9. The method according to claim 7, wherein cosine values ofthe formula are calculated using a sine or cosine table.
 10. The methodaccording to claim 1, wherein the signal is a multi-carrier signal. 11.The method according to claim 10, wherein the signal is a discrete tonemodulated signal.
 12. A method for reducing the crest factor of asignal, said method using a plurality of partial correction signalshaving respective predetermined frequencies, said method comprising: (a)determining a time position of a maximum absolute amplitude of thesignal, (b) calculating an amplitude and a phase for the respectivepartial correction signal depending on said maximum absolute amplitudeand said time position determined in step (a), (c) subtracting therespective partial correction signal from said signal to obtain apartially corrected signal which is used as the signal in step (a) forthe next one of the plurality of partial correction signals, andreturning to step (a) for calculating an amplitude and a phase for thenext partial correction signal, and (d1) calculating a full correctionsignal as a superposition of said plurality of partial correctionsignals, (d2) subtracting the full correction signal from said signal toobtain the corrected signal having the reduced crest factor, and (d3)outputting said corrected signal are performed.
 13. A method forreducing the crest factor of a signal, said method using a plurality ofpartial correction signals having respective predetermined frequencies,said method comprising: (a) determining a time position of a maximumabsolute amplitude of the signal, (b1) calculating an amplitude and aphase for the respective partial correction signal depending on saidmaximum absolute amplitude and said time position determined in step(a), (b2) storing the calculated amplitude and phase values, (c)subtracting the respective partial correction signal from said signal toobtain a partially corrected signal which is used as the signal in step(a) for the next one of the plurality of partial correction signals, andreturning to step (a) for calculating an amplitude and phase for thenext partial correction signal, wherein steps (a) to (c) are repeatedfor at least two iterations for each one of the plurality of partialcorrection signals, and (d1) calculating a plurality of further partialcorrection signals having the respective redetermined frequency, eachone as a superposition of the partial correction signals having therespective predetermined frequency in the stored phases and amplitudescalculated in steps (d) for this frequency, (d2) subtracting theplurality of further partial correction signals from said signal toobtain the corrected signal, and (d3) outputting said corrected signal.14. A method for reducing the crest factor of a signal, said methodusing a plurality of partial correction signals having respectivepredetermined frequencies, said method comprising: (a) determining atimed position of a maximum absolute amplitude of the signal, (b)comparing the maximum absolute amplitude determined in step (a) with apredetermined value, wherein if the maximum absolute amplitude is abovethe predetermined value the following steps are preformed; (c)calculating an amplitude and a phase for the respective partialcorrection signal depending on said maximum absolute amplitude and saidtime position determined in step (a), (d) subtracting the respectivepartial correction signal from said signal to obtain a partiallycorrected signal which is used as the signal in step (a) for the nextone of the plurality of partial correction signals, and returning tostep (a) for calculating an amplitude and a phase for the next partialcorrection signal, and (e) outputting the last obtained partiallycorrected signal as the corrected signal having the reduced crestfactor, and wherein if the maximum absolute amplitude is below thepredetermined value, the following step is preformed; (f) outputting thesignal.
 15. A method for reducing the crest factor of a signal, whereinthe signal is a sampled signal represented as a signal vector of Nsignal values at N sampling times, said method using a plurality ofpartial correction vectors having respective predetermined frequencies,said method comprising: (a1) forming a first auxiliary vector containingas elements M signal values having the M largest absolute values of theN signal values, M being smaller than N, (a2) forming a second auxiliaryvector indicating the positions of the elements of the first auxiliaryvector in the signal vector, (a3) determining a time position of amaximum absolute amplitude of the first auxiliary vector using phaseinformation of the second auxiliary vector, (b) calculating an amplitudeand a phase for a respective partial correction vector depending on saidmaximum absolute amplitude and said time position determined in step(a3), (c) subtracting the respective partial correction vector from thefirst auxiliary vector to obtain a partially connected vector which isused as the first auxiliary vector in step (a3) for the next one of theplurality of partial correction vector, and returning to step (a3) forcalculating an amplitude and a phase for the next partial correctionvector, (d1) calculating a correction vector for the signal vector basedon said amplitudes and said phases calculated in step (b) translated tophases for the signal vector using the second auxiliary vector, (d2)subtracting said correction vector from said signal vector to obtain acorrected signal vector, and (d3) outputting a signal corresponding tosaid corrected signal vector as the corrected signal having the reducedcrest factor.
 16. The method according to claim 15, wherein step (b)comprises the steps of (b1) calculating said amplitude according toA=g·(max {xm(k)·cos(2πμ(pm(k)−pm(k max))/ N)}++min{xm(k)·cos(2πμ(pm(k)−pm(k max))/N)}), A being the amplitude, g being apredetermined factor, μ being a number of the respective predeterminedfrequency, k being a number of the sample, k max being the number of thesample at said time position, xm(k) being element k of said firstauxiliary vector, pm(k) being element k of said second auxiliary vector,and (b2) calculating said phase p according to p=2πμ·k max/N.
 17. Themethod according to claim 15, wherein steps (a1) and (a2) comprise thesteps of: (aa1) assigning the M last elements of the signal vector toelements of the first auxiliary vector, (aa2) assigning the M lastsample positions of the signal vector to the elements of the secondauxiliary vector, (aa3) setting a counter to 0, (aa4) determining theelement of the first auxiliary vector having the smallest absoluteamplitude, (aa5) incrementing the counter by 1, (aa6) checking if theelement of the signal vector designated by the counter has a largerabsolute amplitude than the element of the first auxiliary vector havingthe smallest absolute amplitude, and, if not, returning to step (aa5),(aa7) replacing the element of the first auxiliary vector having thesmallest absolute amplitude by the element of the signal vectordesignated by the counter, and replacing the corresponding element ofthe second auxiliary vector by the counter, (aa8) returning to step(aa4) until the counter has reached N−M.
 18. An apparatus for reducingthe crest factor of a signal using a plurality of partial correctionsignals having respective predetermined frequencies, said apparatuscomprising processing means designed to carry out, for each one of saidpartial correction signals, the steps of: (a) determining a timeposition of a maximum absolute amplitude of the signal, (b) calculatingan amplitude and a phase for the respective partial correction signaldepending on said maximum absolute amplitude and said time positiondetermined in step (a), (c) subtracting the respective partialcorrection signal from said signal to obtain a partially correctedsignal which is used as the signal in step (a) for the next one of theplurality of partial correction signals, and returning to step (a) forcalculating an amplitude and a phase for the next partial correctionsignal, said apparatus further comprising output means for outputtingthe last obtained partially corrected signal as the corrected signalhaving the reduced crest factor.
 19. The apparatus according to claim18, wherein the processing means are designed to repeat steps (a) to (c)for at least two iterations for each one of the plurality of partialcorrection signals.
 20. The apparatus according to claim 19, where amaximum number of iterations is predetermined.
 21. The apparatusaccording to claim 19, said apparatus further comprising comparisonmeans for comparing a maximum absolute amplitude of said partiallycorrected signal with a predetermined value, said comparison means beingcoupled with said processing means such that steps (a) to (c) arerepeated for each one of the plurality of partial correction signalsuntil said maximum absolute amplitude of the partially corrected signalis below said predetermined value.
 22. The apparatus according to claim19, further comprising storage means for storing the calculatedamplitude and phase values in step (b), and wherein the outputting meansare designed such that they perform the steps of (d1) calculating aplurality of further partial correction signals having the predeterminedfrequencies each as a superposition of the partial correction signalshaving the respective predetermined frequency phases and amplitudesstored in the storage means for this frequency (d2) subtracting theplurality of further partial correction signals from said signal toobtain the corrected signal, and (d3) outputting said corrected signal.23. The apparatus according to claim 18, wherein the processing meansare designed such that they carry out in step (b) the steps of (b1)calculating said amplitude according toA=g·(max {x(t)·cos(2 πf(t−t max))}+min {x(t)·cos(2πf(t−t max))}), Abeing the amplitude, g being a predetermined factor, f being therespective predetermined frequency, t being the time, t max being saidtime position and x(t) being said signal, and (b2) calculating saidphase p according to p=2πf·t max.
 24. The apparatus according to claim18, wherein the signal is a sampled signal represented as a signalvector of N signal values at N sampling times.
 25. The apparatusaccording to claim 24, wherein said apparatus comprising preprocessingmeans for preprocessing said signal vector according to the steps of(a1) forming a first auxiliary vector containing as elements the Msignal values having the M largest absolute values of the N signalvalues, M being smaller than N, (a2) forming a second auxiliary vectorindicating the positions of the elements of the first auxiliary vectorin the signal vector, wherein the preprocessing means are coupled to theprocessing means so that the processing means perform the steps (a) to(c) on the first auxiliary vector instead of on the signal using phaseinformation of the second auxiliary vector, and wherein the outputtingmeans are designed to carry out the steps of (d1) calculating acorrection vector for the signal vector based on said amplitudes andsaid phases calculated in step (b) translated to phases for the signalvector using the second auxiliary vector, (d2) subtracting saidcorrection vector from said signal vector to obtain a corrected signalvector, and (d3) outputting a signal corresponding to said correctedsignal vector as the corrected signal having the reduced crest factor.26. The apparatus according to claim 25, wherein the processing meansare designed to carry out, in step (b), the steps of (b1) calculatingsaid amplitude according toA=g·(max {xm(k)·cos(2πμ(pm(k)−pm(k max))/N)}++min{xm(k)·cos(2πμ(pm(k)−pm(k max))/N)}), A being the amplitude, g being apredetermined factor, μ being a number of the respective predeterminedfrequency, k being a number of the sample, k max being the number of thesample at said time position, xm(k) being element k of said firstauxiliary vector, pm(k) being element k of said second auxiliary vector,and (b2) calculating said phase p according to p=2πμ·k max/N.
 27. Theapparatus according to claim 25, wherein the preprocessing means aredesigned to carry out, in steps (a1) and (a2), the steps of: (aa1)assigning the M last elements of the signal vector to elements of thefirst auxiliary vector, (aa2) assigning the M last sample positions ofthe signal vector to the elements of the second auxiliary vector, (aa3)setting a counter to 0, (aa4) determining the element of the firstauxiliary vector having the smallest absolute amplitude, (aa5)incrementing the counter by 1, (aa6) checking if the element of thesignal vector designated by the counter has a larger absolute amplitudethan the element of the first auxiliary vector having the smallestabsolute amplitude, and, if not, returning to step (aa5), (aa7)replacing the element of the first auxiliary vector having the smallestabsolute amplitude by the element of the signal vector designated by thecounter, and replacing the corresponding element of the second auxiliaryvector by the counter, (aa8) returning to step (aa4) until the counterhas reached N−M.
 28. The apparatus according to claim 24, wherein theprocessing means are designed to carry out, in step (b), the steps of(b1) calculating said amplitude according to the formulaA=g·(max {x(k)·cos(2πμ(k−k max)/N)}+min(x(k)·cos(2πμ(k−k max)/N)}), Abeing the amplitude, g being a predetermined factor, μ being a number ofthe respective predetermined frequency, k being a number of the sample,k max being this number of the sample at said time position, and x(k)being a k-th component of said signal vector, and (b2) calculating saidphase p according to p=2πμ·k max/N.
 29. The apparatus according to claim28, wherein values for μ have the form 2^(l)·v, l and v being integernumbers.
 30. The apparatus according to claim 28, said apparatus furthercomprising a stored sine or cosine table for calculating cosine valuesof the formula.
 31. The apparatus according to claim 18, wherein thesignal is a multi-carrier signal.
 32. The apparatus according to claim31, wherein the signal is a discrete tone modulated signal.
 33. Anapparatus for reducing the crest factor of a signal using a plurality ofpartial correction signals having respective predetermined frequencies,said apparatus comprising: processing means designed to carry out, foreach one of said partial correction signals, the steps of: (a)determining a time position of a maximum absolute amplitude of thesignal, (b) calculating an amplitude and a phase for the respectivepartial correction signal depending on said maximum absolute amplitudeand said time position determined in step (a), (c) subtracting therespective partial correction signal from said signal to obtain apartially corrected signal which is used as the signal in step (a) forthe next one of the plurality of partial correction signals, andreturning to step (a) for calculating an amplitude and a phase for thenext partial correction signal, and output means designed to carry outthe steps of: (d1) calculating a full correction signal as asuperposition of said plurality of partial correction signals, (d2)subtracting the full correction signal from said signal to obtain thecorrected signal having the reduced crest factor, and (d3) outputtingsaid corrected signal.
 34. An apparatus for reducing the crest factor ofa signal using a plurality of a partial correction signals havingrespective predetermined frequencies, said apparatus comprising:processing means designed to carry out, for each one of said partialcorrection signals, the step of: (a) determining a time position of amaximum absolute amplitude of the signal, comparison means for comparingthe maximum absolute amplitude determined in step (a) with apredetermined value, said comparison means being coupled with theprocessing means, and output means coupled to the comparison means,wherein if the maximum absolute amplitude is above the predeterminedvalue the processing means performs: (b) calculating an amplitude and aphase for the respective partial correction signal depending on saidmaximum absolute amplitude and said time position determined in step(a), (c) subtracting the respective partial correction signal from saidsignal to obtain a partially corrected signal which is used as thesignal in step (a) for the next one of the plurality of partialcorrection signals, and returning to step (a) for calculating anamplitude and a phase for the next partial correction signal, and theoutput means outputs the last obtained partially corrected signal as thecorrected signal having the reduced crest factor, and wherein if themaximum absolute amplitude is below the predetermined value, the outputmeans outputs the signal.